c-------------------------------------------------------------------------
      subroutine F_11 (res, a, b, z, eps)
      real*8  eps
      complex*16 a, b, z, t1, a1, b1, f, one, res
      one = dcmplx(1d0, 0d0)
      Res = one
c
c     If  z.gt.1, there is another formular with (1/z)^n, but it diverges!!
      f = one
      t1 = a * z / b
      a1 = a
      b1 = b
      do while (real(abs(t1)) .gt. eps)
         Res = Res + t1
         a1 = a1 + 1
         b1 = b1 + 1
         f  = f  + 1
         t1 = t1 * a1 * z / (b1 * f)
      end do 
c$$$      print*, abs(f)
      return
      end
c-------------------------------------------------------------------------
      function F_21 (a, b, c, z, eps)
      real*8  eps
      complex*16 a, b, c, z, t1, a1, b1, c1, f, one, res, f_21
      one = dcmplx(1d0, 0d0)
      res = one
c
c     If  z.gt.1, there is another formular with (1/z)^n, but it diverges!!
      f = one
      t1 = a * b * z / c
      a1 = a
      b1 = b
      c1 = c
      do while (real(abs(t1)) .gt. eps)
         res = res + t1
         a1 = a1 + one
         b1 = b1 + one
         c1 = c1 + one
         f  = f  + one
         t1 = t1 * a1 * b1 * z / (c1 * f)
      end do 
c$$$      print*, abs(f)
      f_21 = res
      return
      end
c------------------------------------------------------------
